Horizontally Scalable Submodular Maximization

TL;DR

This paper introduces a scalable distributed approach for submodular maximization that works under fixed machine capacity, providing theoretical guarantees and competitive empirical performance compared to centralized methods.

Contribution

It presents a novel framework for distributed submodular maximization that remains effective under fixed capacity constraints, unlike previous methods.

Findings

Achieves approximation guarantees for fixed capacity scenarios.

Performs competitively with centralized greedy algorithms in experiments.

Applicable to a broad class of algorithms and constraints.

Abstract

A variety of large-scale machine learning problems can be cast as instances of constrained submodular maximization. Existing approaches for distributed submodular maximization have a critical drawback: The capacity - number of instances that can fit in memory - must grow with the data set size. In practice, while one can provision many machines, the capacity of each machine is limited by physical constraints. We propose a truly scalable approach for distributed submodular maximization under fixed capacity. The proposed framework applies to a broad class of algorithms and constraints and provides theoretical guarantees on the approximation factor for any available capacity. We empirically evaluate the proposed algorithm on a variety of data sets and demonstrate that it achieves performance competitive with the centralized greedy solution.